Smalling will stay at the Stadio Olimpico for the rest of the Serie A season, which is currently scheduled to last until the beginning of August, due to the effects of the COVID-19 pandemic.
Alexis's deal at Inter Milan has also been extended until the end of the first week of next month.
Smalling, who marks 10 years as a United player this summer, has featured for the Romans on 30 occasions this season, scoring two goals.
Alexis has overcome an injury setback to play 19 games for Antonio Conte's Inter, who also boast former Reds Romelu Lukaku and Ashley Young in their ranks.